ADI Method for Sylvester Equations January 28, 2011 3:00 p.m. Ren-Cang Li Abstract We are concerned with numerical solutions of large scale Sylvester equations AX XB = C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li and White (2002) demonstrated […]
Using Algebraic Multigrid For Numerical Upscaling October 13, 2010 2:30 p.m. Panayot S. Vassilevski Abstract We will give an introduction to multigrid methods (or MG) for solving systems of (linear) algebraic equations. We will first give a motivation why the method has the potential to be of optimal order, namely, that it can be […]
Taxonomy for the Automated Tuning of Matrix Algebra Software September 10, 2010 4:00 p.m. Dr. Elizabeth R. Jessup Abstract Linear algebra constitutes the most time-consuming part of simulations in many fields of science and engineering. Reducing the costs of those calculations can have a significant impact on overall routine performance, but such optimization is […]
Discontinuous Petrov-Galerkin Method for Steady Transport March 28, 2011 3:30 p.m. Victor Calo Abstract The objective of this work is to analyze and develop discontinuous Petrov-Galerkin (DPG) methods in context of isogeometric analysis. The DPG framework enables an automatic computation of test function spaces that guarantee numerical stability whereas isogeometric analysis aims at the […]
Construction of High Order Schemes for the Compressible Euler and Navier-Stokes Equations August 26, 2011 11:00 a.m. Remi Abgrall Abstract In this talk, I shall describe and analyze a class of finite element schemes that are able to compute solutions of the Euler or Navier-Stokes equations that may present very sharp gradients. The connection with […]